2026/07/20 by Özgür Akarsu, Antonio De Felice, N. Merve Uzun
#gr-qc #astro-ph.CO
In general relativity, cosmic acceleration is timelike defocusing of the comoving congruence and requires a negative total active gravitational mass density, M\rm tot=ρ\rm tot+3p\rm tot<0. The criterion w≡ p/ρ<-1/3 diagnoses sector repulsion only for ρ>0: the inequality reverses for ρ<0, and ratio variables are ill-defined at ρ=0 even when the stress-energy tensor is finite. For sign-changing effective dark energy (DE), as in Λ\rm sCDM-type histories, we instead use the signed density ρ\rm de and two branch-independent combinations. The regular null energy condition (NEC) boundary I\rm de=ρ\rm de+p\rm de=0 replaces the phantom divide w\rm de=-1, while M\rm de=ρ\rm de+3p\rm de<0 governs sector-level Raychaudhuri repulsion. For a separately conserved DE sector with a smooth negative-to-positive density crossing of finite odd order n at z_†, we prove that I\rm de and M\rm de are negative in a punctured neighborhood and non-positive at the crossing, while w\rm de develops a kinematic pole with universal residue n(1+z_†)/3. If M\rm de>0 at some sufficiently high redshift, continuity requires at least one repulsion boundary z\rm rep>z_†: the sector is already repulsive while ρ\rm de<0. We derive the exact range of ρ\rm de'(z_†) for acceleration at the crossing with the total NEC satisfied. Under the stated single-impulse and stationary-point assumptions, the deceleration parameter has one or three sign-changing zeros. A smooth Λ\rm sCDM profile, an exponential infrared f(T) model, and the minimal phantom brane illustrate the results. These results motivate organizing late-time inference around (ρ,p,I,M) rather than around w alone.